Frequency Relationships of Air Pollution: a Case Study for PM2.5

International Journal of Environmental Research and Public Health

Article Establishment of Regional Concentration–Duration– Frequency Relationships of Air Pollution: A Case Study for PM2.5

Hone-Jay Chu * and Muhammad Zeeshan Ali

Department of Geomatics, National Cheng Kung University, Tainan 70101, Taiwan; [email protected] * Correspondence: [email protected]

Received: 5 February 2020; Accepted: 19 February 2020; Published: 22 February 2020

Abstract: Poor air quality usually leads to PM2.5 warnings and affects human health. The impact of frequency and duration of extreme air quality has received considerable attention. The extreme concentration of air pollution is related to its duration and annual frequency of occurrence known as concentration–duration–frequency (CDF) relationships. However, the CDF formulas are empirical equations representing the relationship between the maximum concentration as a dependent variable and other parameters of interest, i.e., duration and annual frequency of occurrence. As a basis for deducing the extreme CDF relationship of PM2.5, the function assumes that the extreme concentration is related to the duration and frequency. In addition, the spatial pattern estimation of extreme PM2.5 is identified. The regional CDF identifies the regional extreme concentration with a specified duration and return period. The spatial pattern of extreme air pollution over 8 h duration shows the hotspots of air quality in the central and southwestern areas. Central and southwestern Taiwan is at high risk of exposure to air pollution. Use of the regional CDF analysis is highly recommended for efficient design of air quality management and control.

Keywords: PM2.5; duration; frequency; spatial map

1. Introduction Air pollution has become a worldwide environmental health risk [1,2], especially in the developing countries. In management, an essential task is to understand the duration, frequency, and intensity of air pollution [3,4]. Poor air quality usually affects human health [5–7]. Elderly people, children, and people with heart or lung conditions are more sensitive than others to the effects of inhaling fine particles (PM2.5). Acute exposure to PM2.5 is associated with various health outcomes, such as respiratory symptoms [8,9], hospital admissions, or death [10]. The maximum PM2.5 concentrations have significant positive impacts on outpatient visits [11]. Chronic exposure to PM2.5 can lead to chronic diseases or reduced life expectancy [12]. The risk that extreme pollutant concentrations pose to human health is the subject of environmental concern [10]. The impact of frequency and duration of air quality has received considerable attention over the past decades. However, few people discuss the concentration–duration–frequency (CDF) relationships in air pollution. The CDF is modified from the intensity–duration–frequency (IDF) relationship, which is a mathematical relationship between the rainfall intensity, duration, and annual frequency of occurrence [13]. The most common IDF techniques from hydrological engineering were used for Gumbel distribution [14]. However, the CDF is related to the extreme concentration of air pollution with its duration and annual frequency of occurrence. The CDF formulas are empirical equations representing a relationship between the maximum concentration as a dependent variable and other parameters of interest, i.e., duration and annual frequency of occurrence. In the frequency aspect, the

Int. J. Environ. Res. Public Health 2020, 17, 1419; doi:10.3390/ijerph17041419 www.mdpi.com/journal/ijerph Int. J. Environ. Res. Public Health 2020, 17, 1419 2 of 13 return period of an event might be 100 years and is expressed as its probability of occurring being 1/100, or 1% in any one year. Many types of distributions, such as log-normal, Weibull, Pearson, gamma, and Gumbel distributions, are used to fit the distribution of air pollutant concentration [10,15–18]. The probability of occurrence and the CDF of extreme PM2.5 can be investigated using standard statistical techniques, e.g., Gumbel, log-normal, and Weibull probability distributions. In this study, the CDF analysis of fine aerosols was performed using the Gumbel probability distribution. The analysis system uses the actual measurement records to calculate the occurrence values of different frequencies according to the statistical properties of the samples and presumes the possible devaluation values to derive the basis of the extreme CDF relationship. Moreover, the empirical CDF relationship in this study is assumed to be the Bernard formula function [13,19]. The coefficient estimation is performed in a regression, and the estimated extreme concentration based on the defined return period and duration is finally obtained. The CDF analysis for a single station can be derived from historical data of PM2.5. However, the spatial pattern of air pollution is heterogeneous [20]. The regional CDF function is developed and determined on the basis of the regional parameters. Based on interpolation, the regional parameters can be estimated. The regional CDF analysis provides spatial patterns of extreme air pollution and further provides detailed spatial patterns in areas where no observations are available. The model estimates the extreme concentrations at unknown locations by simultaneously considering the regional parameters and using the regional CDF function as proxy information to provide information on the relationships of spatial patterns of air quality with various durations and return periods. Using the regional CDF analysis, the hotspot area of air pollution with a specified duration and return period can be identified. The objective of the study was to develop the relationship between the extreme PM2.5 concentration, the duration, and the frequency of occurrence. As a basis for deducing the Gumbel extreme value distribution and the empirical CDF model, the extreme concentration was assumed to be related to the duration and frequency, and the coefficient estimation was carried out in a regression. Furthermore, regional CDF estimations were conducted. It was expected that the regional CDF would identify the regional extreme concentration map with a specified duration and return period.

2. Materials and Study Area Figure1 shows the locations of air quality monitoring stations in Taiwan. Air quality zones, e.g., northern, central, southwestern, and eastern, are also established in Taiwan (Figure1). The Taiwanese Environmental Protection Agency (TWEPA) has been regularly recording the air quality and meteorological data throughout Taiwan since July 1982 [20]. Since August 2005, the TWEPA has completed the installation of 76 monitoring instruments for ﬁne airborne aerosols (PM2.5; Figure1). In this study, the historical data obtained by the TWEPA’s Air Monitoring Network were obtained for the PM2.5 hourly ﬁne aerosol concentration in Taiwan from 2005 to 2015. This study used the hourly PM2.5 obtained by the TWEPA stations that are in compliance with the regulatory air monitoring procedures. Int. J. Environ. Res. Public Health 2020, 17, 1419 3 of 13 Int. J. Environ. Res. Public Health 2020, 17, x FOR PEER REVIEW 3 of 13

FigureFigure 1.1. LocationsLocations ofof PMPM2.52.5 monitoringmonitoring stations stations..

3.3. Method Methodss

First,First, the moving average ofof PM2.52.5 datadata for for various various durations durations need neededed to be prepared. Derivations of the PM2.5 CCDFDF relationships relationships for for each each station station for for the different diﬀerent return periodsperiods were determined by ﬁttingfitting the Gumbel distribution to the correspondingcorresponding maximum concentration per year at various stations (Section(Section 3.13.1)).. The empirical model for thethe PMPM2.52.5 CDFCDF analysis at each station was developed (Section(Section 3.23.2)).. Eventually, thethe regionalregional PMPM2.52.5 CDF analysis w wasas performed ( (SectionSection 3.3)3.3)..

3.1. Derivations of PM2.5 CDF 3.1. Derivations of PM2.5 CDF The probability of occurrence of the extreme pollution event (C c) for the annual frequency of The probability of occurrence of the extreme pollution event (퐶≥≥ 푐) for the annual frequency F exceedanceof exceedance ( ) ( is퐹) the is the inverse inverse of theof the return return period period calculated calculated as follows:as follows: 11 P푃((C퐶 ≥c푐))==F퐹== (1(1)) ≥ T푇 The probability ofof non-exceedancenon-exceedance isis asas follows:follows: 1 푃(퐶 ≤ 푐) = 1 −1 (2) P(C c) = 1 푇 (2) ≤ − T where 푇 is the return period or recurrence interval of extreme concentration, 퐶 is the extreme PM2.5 whereconcentrationT is the, returnand 푐 is period the threshold or recurrence. interval of extreme concentration, C is the extreme PM2.5 concentration,The Gumbel distribution and c is the was threshold. fitted to the extreme PM2.5 data, i.e., to the maximum annual values. The cumulative Gumbel extreme value distribution is illustrated as follows [21]:

−α(퐶−β) 푃(퐶 ≤ 푐) = 푒−푒 (3)

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The Gumbel distribution was ﬁtted to the extreme PM2.5 data, i.e., to the maximum annual values. The cumulative Gumbel extreme value distribution is illustrated as follows [21]:

e α(C β) P(C c) = e− − − (3) ≤ where P(C c) is the probability of non-exceedance, and α and β are the parameters of the Gumbel ≤ distribution. From the observed sequence, the parameters can be estimated [13]. The parameters α and β are linked to the mean value (C) of the extreme PM2.5 data and to the standard deviation (σC) of the extreme PM2.5 data through the following equations:

1.282 α = (4) σC

0.577σ β = C C = C 0.45σ (5) − 1.282 − C The logarithm was taken twice to yield a formulation from Equation (3), and Equation (2) was merged into Equation (3). Thus, the extreme concentration of PM2.5 (C) for each return period is as follows: 1 C = β ln(lnT ln(T 1)) (6) − α − − In addition, C can be expressed as a function of the return period for each duration. The average extreme concentrations for various durations were calculated based on the aforementioned steps. For the respective periods, the maximum values of 1, 8, 16, 24, 48, and 96 h-average concentrations were used for the modeling. In the speciﬁc duration, the PM2.5 extreme concentration is a function of the return period. The following return periods are considered in this study: 5, 10, 20, 30, 40, 50, 60, 75, and 100 years.

3.2. Empirical PM2.5 CDF Function Based on the above modeling, the empirical CDF formulas can be developed on the basis of the equations representing a relationship between the maximum PM2.5 concentration (C), duration (D), and frequency (F), which is the inverse of the return period (1/T), as follows:

C = f (T, D) (7) where D is the duration. The empirical function follows the power expression based on the Bernard equation [13,19]: a b C = kT D− (8) where k, a, b are the model coefficients. We also consider the natural logarithm of both sides of the equation: lnC = lnk + alnT blnD (9) − The least squares method is applied to determine the parameters of the empirical CDF equation. The parameters of Equation (9) for different return periods (5, 10, 20, 30, 40, 50, 60, 75, and 100 years) and different durations (1, 8, 16, 24, 48, and 96 h) are calculated.

3.3. Regional CDF Mapping of Extreme PM2.5

The empirical PM2.5 CDF function for each station was identiﬁed using Equation (8), whereas the regional CDF model was determined using Equation (10). The regional PM2.5 CDF model is generated from the CDF with spatially varying parameters k(x), a(x), b(x) that are spatially interpolated. Regional concentration C(x) of PM2.5 at any location x is the function within a speciﬁed return period (T) within a duration (D) as follows: a(x) b(x) C(x) = k(x)T D− (10) Int. J. Environ. Res. Public Health 2020, 17, 1419 5 of 13

i.e. lnC(x) = lnk(x) + a(x)lnT b(x)lnD, (11) − where regional coefficients, e.g., k(x), a(x), b(x), at any location x are generated using k, a, b regression parameters by using the inverse distance weighted (IDW). The IDW method is a straightforward and low-computational approach for spatial interpolation procedures [22]. The k(x), a(x), b(x) regional coefficient maps are shown in the Appendix Figure A1. Int. J. Environ. Res. Public Health 2020, 17, x FOR PEER REVIEW 5 of 13 4. Results and Discussion 4.1. Descriptive Statistics and Plots of Extreme PM2.5 Concentration 4.1. Descriptive Statistics and Plots of Extreme PM2.5 Concentration Figure 2 shows the maximum 96 h-average PM2.5 concentration from 2005 to 2015. The maximum, the average valueFigure, and2 shows the thestandard maximum deviation 96 h-average of the PM extreme2.5 concentration data are 147 from, 103 2005, and to 2015. 21 μg/m The maximum,3, 3 respectivelythe. The average extreme value, PM and2.5 concentration the standard is lower deviation in northern of the extremeand eastern data Taiwan are 147, and 103, higher and in 21 µg/m , central andrespectively. southern Taiwan. The extreme This PMresult2.5 concentrationleads to the regionalization is lower in northern of the andCDF eastern relationships Taiwan for and higher various geographicalin central and areas southern. Taiwan. This result leads to the regionalization of the CDF relationships for In thisvarious study, geographical the CDF relation areas.ship (Equations (4) to (6)) was derived for each station, and the empirical CDFIn formulas this study, (Equation the CDF (8 relationship)) can be evaluat (Equationsed with (4)different to (6)) durations was derived and forreturn each periods. station, and the Figure 3 empiricalshows the CDF result formulas plots of (Equation the extreme (8)) can96 h be-average evaluated concentration with different at 5 durations-year and and 100 return-year periods. return periods.Figure 3 In shows the comparison the result plots of various of the extreme return 96 periods, h-average the concentration PM2.5 concentration at 5-year patterns and 100-year are return similar, butperiods. the values In the are comparison different. For of the various 100-year return return periods, period, the the PM m2.5aximum,concentration the average patterns value are, similar, and the standardbut the values deviation are di offferent. the extreme For the 96 100-year h-average return concentrations period, the maximum,are 175, 121 the, and average 25 μg/m value,3, and the standard deviation of the extreme 96 h-average concentrations are 175, 121, and 25 µg/m3, respectively. respectively. The extreme PM2.5 value for the 100-year return periods is 1.5 times of the 5-year ones. PollutionThe hotspots extreme are PMin 2.5thevalue neighboring for the 100-yearcounties returnand cities periods of central is 1.5 and times south of thewestern 5-year Taiwan. ones. Pollution hotspots are in the neighboring counties and cities of central and southwestern Taiwan. Eastern Taiwan Eastern Taiwan contains the lowest concentration of PM2.5. contains the lowest concentration of PM2.5.

3 Figure 2. Average extreme PM concentration within 96 h from 2005 to 2015 (unit:3 µg/m ). Figure 2. Average extreme PM2.5 concentration2.5 within 96 h from 2005 to 2015 (unit: μg/m ).

Figure 3. Average extreme PM2.5 concentration within 96 h for 5-year (a) and 100-year (b) return periods (unit: μg/m3).

4.2. Heterogeneity of Air Pollution

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4.1. Descriptive Statistics and Plots of Extreme PM2.5 Concentration

Figure 2 shows the maximum 96 h-average PM2.5 concentration from 2005 to 2015. The maximum, the average value, and the standard deviation of the extreme data are 147, 103, and 21 μg/m3, respectively. The extreme PM2.5 concentration is lower in northern and eastern Taiwan and higher in central and southern Taiwan. This result leads to the regionalization of the CDF relationships for various geographical areas. In this study, the CDF relationship (Equations (4) to (6)) was derived for each station, and the empirical CDF formulas (Equation (8)) can be evaluated with different durations and return periods. Figure 3 shows the result plots of the extreme 96 h-average concentration at 5-year and 100-year return periods. In the comparison of various return periods, the PM2.5 concentration patterns are similar, but the values are different. For the 100-year return period, the maximum, the average value, and the standard deviation of the extreme 96 h-average concentrations are 175, 121, and 25 μg/m3,

respectively. The extreme PM2.5 value for the 100-year return periods is 1.5 times of the 5-year ones. Pollution hotspots are in the neighboring counties and cities of central and southwestern Taiwan. Eastern Taiwan contains the lowest concentration of PM2.5.

Figure 2. Average extreme PM2.5 concentration within 96 h from 2005 to 2015 (unit: μg/m3). Int. J. Environ. Res. Public Health 2020, 17, 1419 6 of 13

Figure 3. Average extreme PM2.5 concentration within 96 h for 5-year (a) and 100-year (b) return periods (unit: µg/m3). Figure 3. Average extreme PM2.5 concentration within 96 h for 5-year (a) and 100-year (b) return 4.2. Heterogeneityperiods (unit: of μg/m Air3 Pollution). According to the CDF relationship, the PM concentration is high with a low return period. In 4.2. Heterogeneity of Air Pollution 2.5 addition, the decrease of the extreme concentration varies with increasing duration. Figure4 shows the comparison of the CDF curves in Erlin, Xiaogang, and Hualien in western, southwestern, and eastern Taiwan (locations shown in Figure1). For the 5-year return period, the 8 h-average concentration is 110 µg/m3, and the 96 h-average concentration drops to 60 µg/m3 in Hualien. However, in Erlin and Xiaogang, the 8 h-average concentrations are 170 and 175 µg/m3, and the 96 h-average concentrations are only reduced to 100 and 110 µg/m3. Table1 shows the model coe fficient list and illustrates coefficient b for duration containing large differences in the observations. Duration of air pollution is higher in Erlin than in Xiaogang and Hualien. According to the data for the duration over 24 h, air pollution persists in Erlin more than in Xiaogang and Hualien. The CDF curves clearly show the differences between the extreme PM2.5 concentrations in the eastern and the western parts of Taiwan. In Figure4, the downward slope of the CDF curve is greater in Hualien than in Erlin and Xiaogang. Air pollution was generally more serious in the western part when compared with the eastern part of Taiwan. The heterogeneity of extreme pollutant concentrations represents a different level of risk to people’s health [23]. The emissions were from local sources, such as traffic and industrial or agricultural activities, and from outside Taiwan [24,25]. A highly developed industry and a large population density distinguish the western plain of Taiwan. Air quality is mainly influenced by local emission sources over the southwestern and central inland cities of Taiwan, but meteorological conditions also affect air pollution dispersion in Taiwan [26]. Air quality in the urban and industrial regions of southwestern and west central Taiwan is poor in the winter [20]. However, traffic and industrial activities are low in eastern Taiwan. The air quality in eastern Taiwan is generally good. In addition, emission sources, meteorological conditions, and atmospheric boundary layers affect transmission and diffusion of air pollution [27,28]. Using the CDF curve and results of the regional CDF analysis, the effect of the PM2.5 emission due to the diffusion differences in various locations can be determined. Int. J. Environ. Res. Public Health 2020, 17, 1419 7 of 13 Int. J. Environ. Res. Public Health 2020, 17, x FOR PEER REVIEW 7 of 13

FigureFigure 4. CDF4. CDF curves curve ins in (a) ( Erlin,a) Erlin (b, )(b Hualien,) Hualien and, and (c) ( Xiaogangc) Xiaogang for for the the duration duration of 8–96of 8–96 h. h.

4.3. Regional CDF Analysis Short- and long-return period air pollutions, such as 5-year and 100-year ones, provided the difference in frequencies of local high pollution levels and the effects of spatial PM2.5 patterns. Figures

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Table 1. R2, root-mean-square error (RMSE), and coeﬃcients (k, a, b) of the concentration–duration– frequency (CDF) empirical model.

Erlin Hualien Xiaogang k 182.151 283.163 259.355 a 0.118 0.108 0.092 b 0.154 0.424 0.219 R2 0.98 0.98 0.99 RMSE (µg/m3) 2.9 3.9 1.4

4.3. Regional CDF Analysis Short- and long-return period air pollutions, such as 5-year and 100-year ones, provided the difference in frequencies of local high pollution levels and the effects of spatial PM2.5 patterns. Figures5 and6 show the estimated extreme concentration for 5-year and 100-year return periods with the duration of 1, 8, 24, and 96 h. If the analyzed duration was 1 h, the few, local, and distributed hotspots were from the northern, central, and southwestern areas of Taiwan, respectively. This anomaly in air quality may have been caused by a local event, e.g., a fireworks festival, agricultural and domestic solid fuel burning, or a forest wildfire. Over 8 h, the spatial pattern of air pollution was highly similar. The greater the duration, the larger the hotspot. The PM2.5 exposure is not randomly distributed. The hotspots of PM2.5 air pollution were shown in the central area and in the southwestern area of Taiwan, especially at the 96 h duration. The long-duration air pollution in Taiwan is usually the effect of local sources, topography, and the monsoon [20]. The current northeast monsoon is weakening, leading to poor diffusion conditions to drive air pollutants [29]. Air quality becomes poor due to stagnant conditions in western Taiwan, particularly in central and southern Taiwan. Previous research also found that elevated total ambient PM2.5, due to poor diffusion conditions as the northeast monsoon weakens, may be associated with acute health outcomes [30]. In general, the PM2.5 concentration in the summer is low, but high in winter. Air pollution in the short term (acute) and in the long term (chronic) should be considered [31,32]. Studies suggest that public health impacts of air pollution will be dominated by short-term and long-term exposure as determined by the association between exposure and mortality [6,31,33,34]. According to the spatial results, central and southwestern Taiwan is at high risk of long-duration exposure of air pollution. These areas are unhealthy for groups who are sensitive to air pollution. Extreme pollution events were observed frequently by monitoring the network. The 1 h-average PM2.5 concentrations reach very high levels. Furthermore, industry and traffic emissions [35], agricultural burning [36], massive incense burning [37], dust storms [38], domestic solid fuel burning [39], and wildfires [30] significantly affect local extreme air pollution. Pollutants released into the environment are spatially fluctuating rather than uniformly distributed, and thus the health risk due to air pollution is an issue of spatial variability [23,40]. This study can provide the information on air pollution distribution with a specified return period and duration. Int. J. Environ. Res. Public Health 2020, 17, x FOR PEER REVIEW 8 of 13

5 and 6 show the estimated extreme concentration for 5-year and 100-year return periods with the duration of 1, 8, 24, and 96 h. If the analyzed duration was 1 h, the few, local, and distributed hotspots were from the northern, central, and southwestern areas of Taiwan, respectively. This anomaly in air quality may have been caused by a local event, e.g., a fireworks festival, agricultural and domestic solid fuel burning, or a forest wildfire. Over 8 h, the spatial pattern of air pollution was highly similar. The greater the duration, the larger the hotspot. The PM2.5 exposure is not randomly distributed. The hotspots of PM2.5 air pollution were shown in the central area and in the southwestern area of Taiwan, especially at the 96 h duration. The long-duration air pollution in Taiwan is usually the effect of local sources, topography, and the monsoon [20]. The current northeast monsoon is weakening, leading to poor diffusion conditions to drive air pollutants [29]. Air quality becomes poor due to stagnant conditions in western Taiwan, particularly in central and southern Taiwan. Previous research also found that elevated total ambient PM2.5, due to poor diffusion conditions as the northeast monsoon weakens, may be associated with acute health outcomes [30]. In general, the PM2.5 concentration in the summer is low, but high in winter. Air pollution in the short term (acute) and in the long term (chronic) should be considered [31,32]. Studies suggest that public health impacts of air pollution will be dominated by short-term and long-term exposure as determined by the association between exposure and mortality [6,31,33,34]. According to the spatial results, central and southwestern Taiwan is at high risk of long- duration exposure of air pollution. These areas are unhealthy for groups who are sensitive to air pollution. Extreme pollution events were observed frequently by monitoring the network. The 1 h-average PM2.5 concentrations reach very high levels. Furthermore, industry and traffic emissions [35], agricultural burning [36], massive incense burning [37], dust storms [38], domestic solid fuel burning [39], and wildfires [30] significantly affect local extreme air pollution. Pollutants released into the environment are spatially fluctuating rather than uniformly distributed, and thus the health risk due to air pollution is an issue of spatial variability [23,40]. This study can provide the information on air pollutionInt. J. Environ.distribution Res. Public with Health a specified2020, 17, 1419return period and duration. 9 of 13

Int. J. Environ. Res. Public Health 2020, 17, x FOR PEER REVIEW 9 of 13 Figure 5. Estimated 1 h- (a), 8 h- (b), 24 h- (c), and 96 h- (d) average extreme PM2.5 concentration for 3 Figurethe 5. 5-year Estimated return 1 h period- (a), 8 (unit: h- (b),µ g24/m h-). (c), and 96 h- (d) average extreme PM2.5 concentration for the 5-year return period (unit: μg/m3).

Figure 6. Estimated 1 h- (a), 8 h- (b), 24 h- (c), and 96 h- (d) average extreme PM2.5 concentration for Figurethe 6. 100-yearEstimated return 1 h- ( perioda), 8 h- (unit: (b), 24µ gh/-m (3c).), and 96 h- (d) average extreme PM2.5 concentration for the 100-year return period (unit: μg/m3). 4.4. Discussion 4.4. DiscussionThe CDF, or the regional CDF method, belongs to the spatiotemporal data analysis of extreme ThePM2.5 CDconcentrationF, or the regional data. SpatiotemporalCDF method, belongs data analysis to the andspatiotemporal visualization data are important analysis of for extreme air pollution PM2.5management concentration [41 data]. However,. Spatiotemporal the summary data of analysis the extreme and pollution visualization data, are or dataimportant analysis, for is air critical. pollutionThe CDFmanagement analysis can[41] help. However, us summarize the summary the main of the characteristics extreme pollution and patterns data, or of data air pollution analysis, for a is critical.speciﬁed Theduration CDF ana andlysis frequency can help and us provide summarize information the main about characteristics the occurrence and of patterns limit exceedances of air pollutionof air for pollution a specified [10]. duration The CDF and curves frequency and their and spatial provide maps information can be used about for areathe delineation,occurrence of policy limit exceedances of air pollution [10]. The CDF curves and their spatial maps can be used for area delineation, policy control, and management [42,43]. The framework is relatively practical, but the experiment proves that it is valid to analyze the extreme air pollution monitoring results with various durations and return periods. The method is used to determine the multiple functions of the CDF in the air pollution data. However, the history of records can help define the long-term behavior. We will maintain the data size as large as possible, and a future study will update the results. Heterogeneity of PM2.5 is highly related to pollutant sources, geographical location, and climatic and topographic conditions [44]. The use of the regional model rather than those for individual stations logically provides more spatial information for management purposes. The extreme PM2.5 concentration was generally spatially varied. Moreover, the regional PM2.5 CDF map could be useful in order to detect the spatial variation of health risk, and the CDF of various durations is needed to determine the health risk [45]. Avoiding exposure to air pollutants is especially critical for the elderly, children, and susceptible individuals with cardiovascular or pulmonary diseases (CVD or COPD) [32]. A further study can be conducted to determine the long-duration concentrations of PM2.5, such as the 1-week-, 10-day-, and 1-month-average concentrations. We will apply the CDF to high- frequency and massive low-cost sensor data, such as airbox data [46,47], and identify the differences.

5. Conclusions

This study presented the derivation of the CDF curves of fine aerosols, PM2.5. The Bernard formula was applied as the basis for estimating the empirical CDF relationship. The empirical CDF curve coefficients were estimated by regressions. Moreover, the regional map for the CDF analysis

Int. J. Environ. Res. Public Health 2020, 17, 1419 10 of 13 control, and management [42,43]. The framework is relatively practical, but the experiment proves that it is valid to analyze the extreme air pollution monitoring results with various durations and return periods. The method is used to determine the multiple functions of the CDF in the air pollution data. However, the history of records can help deﬁne the long-term behavior. We will maintain the data size as large as possible, and a future study will update the results. Heterogeneity of PM2.5 is highly related to pollutant sources, geographical location, and climatic and topographic conditions [44]. The use of the regional model rather than those for individual stations logically provides more spatial information for management purposes. The extreme PM2.5 concentration was generally spatially varied. Moreover, the regional PM2.5 CDF map could be useful in order to detect the spatial variation of health risk, and the CDF of various durations is needed to determine the health risk [45]. Avoiding exposure to air pollutants is especially critical for the elderly, children, and susceptible individuals with cardiovascular or pulmonary diseases (CVD or COPD) [32]. A further study can be conducted to determine the long-duration concentrations of PM2.5, such as the 1-week-, 10-day-, and 1-month-average concentrations. We will apply the CDF to high-frequency and massive low-cost sensor data, such as airbox data [46,47], and identify the diﬀerences.

5. Conclusions

This study presented the derivation of the CDF curves of fine aerosols, PM2.5. The Bernard formula was applied as the basis for estimating the empirical CDF relationship. The empirical CDF curve coefficients were estimated by regressions. Moreover, the regional map for the CDF analysis can be identified based on regional parameters. Results of the preliminary analysis of the data for 2005–2015 showed that the spatial pattern of extreme air pollution was highly similar over an 8 h duration. The local pattern of air pollution lasting for 1 h may be caused by a local event, e.g., a fireworks festival, agricultural and domestic solid fuel burning, and forest wildfires. The greater the duration, the larger the hotspot. Moreover, the use of regional maps rather than those for individual stations provide spatial information on air pollution, particularly for longer durations. Using the regional extreme concentration with a specified duration and return period, the spatial pattern of air pollution showed the hotspots of air pollution in the central area and in the southwestern area of Taiwan. Central and southwestern Taiwan is at high risk of long-duration exposure of air pollution. In addition, the CDF relationship between the stations in western and eastern Taiwan revealed air quality differences between these areas. With the same return period, the concentration was lower in the eastern than in the western part. Air pollution persisted in the western part rather than in the eastern part. Furthermore, the local and the regional CDF relationships proposed in this study can be used as a reference for health planning and management. Further study can be conducted for air quality design and control of pollution.

Author Contributions: H.-J.C.: Conceptualization, Data curation, Formal analysis, Methodology, Writing—original draft, M.Z.A.: Validation, Visualization. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by MOST under grant number 108-2621-M-006-010-. Acknowledgments: The authors would like to thank the MOST of Taiwan for financial support under grant number 108-2621-M-006-010-. The authors would like to thank the editors and anonymous reviewers for providing suggestions for paper improvement. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A The k(x), a(x), b(x) coeﬃcients from Equation (10) are estimated using the IDW. Int.Int. J. Environ. J. Environ. Res. Res. Public Public Health Health 20202020, 17, ,17 x ,FOR 1419 PEER REVIEW 11 11 of of13 13

Figure A1. (a) k(x),(b) a(x),(c) b(x) coeﬃcient maps. Figure A1. (a)ｋ(푥), (b) a(x), (c) b(x) coefficient maps. References

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